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Linearity Characterization and Uncertainty Quantification of Spectroradiometers via Maximum Likelihood and the
Adam L Pintar1, Zachary H Levine2, Howard W Yoon3
1Statistical Engineering Division, National Institute of Standards and Technology, Gaithersburg, Maryland 20899-8980 USA.
Metrologia
|February 21, 2024
Summary
This study introduces a robust uncertainty quantification method for the flux-addition technique, enhancing radiometric instrument linearity calibration. The new approach ensures accurate flux and coefficient estimation with reliable confidence intervals.
Area of Science:
- Metrology and Scientific Instrumentation
- Radiometry and Photometry
- Statistical Modeling and Data Analysis
Background:
- Radiometric instruments require accurate linearity characterization and correction for reliable measurements.
- Existing techniques, such as the flux-addition method (combinatorial technique), lack rigorous uncertainty quantification.
- Nonlinear responses in instruments can significantly impact measurement accuracy.
Purpose of the Study:
- To develop and validate a rigorous uncertainty quantification method for the flux-addition technique.
- To apply the method to both synthetic and experimental data from a beam conjoiner instrument.
- To enable precise calibration of radiometric instruments, including estimation of nonlinear response uncertainties.
Main Methods:
- Development of a probabilistic model linking instrument readout to unknown fluxes via polynomial coefficients.
- Utilizing Maximum Likelihood Estimates (MLEs) for unknown fluxes and polynomial coefficients.
- Employing a non-parametric bootstrap algorithm for uncertainty quantification (standard errors, confidence intervals).
Main Results:
- Validated the method using synthetic radiometric instrument data, showing approximately unbiased MLEs.
- Bootstrap-derived confidence intervals demonstrated consistency with the target 95% coverage for fluxes.
- Observed confidence interval coverages for polynomial coefficients ranged from 91% to 99%.
- Experimental data demonstrated complete calibration with uncertainties, with nonlinear response uncertainty <0.025%.
Conclusions:
- The developed uncertainty quantification method provides a rigorous framework for the flux-addition technique.
- The method effectively characterizes and corrects radiometric instrument linearity with quantifiable uncertainties.
- This approach significantly enhances the reliability and accuracy of radiometric measurements.
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